Dynamical Analysis on the Model of Tuberculosis Spread with Vaccination and Saturated Incident Rate

Abstract

This research concern with dynamical analysis of a SVLIT (Susceptible Vaccination Latent Infective Treatment) model. It represents the spread of tuberculosis with vaccination and saturated incident rate. The incident rate is considered because of the barriers effect due to changes in susceptible individuals behavior. This model has two equilibrium points, namely disease-free equilibrium point which always exists and an endemic equilibrium point that exists under some certain conditions. The local stability of the equilibrium points is investigated by using Routh-Hurwitz criteria. The method of next generation matrix is applied to determine the basic reproduction number R 0. It can be shown numerically that disease-free equilibrium point is local asymptotically stable when R 0 < 1, while the endemic equilibrium point exist and local asymptotically stable when R 0 > 1. Numerical simulations are given to illustrate the theoretical results.